gdist {mvpart}R Documentation

Dissimilarity Measures

Description

The function computes useful dissimilarity indices which are known to have a good rank-order relation with gradient separation and are thus efficient in community ordination with multidimensional scaling.

Usage

gdist(x, method="bray", keepdiag=FALSE, full=FALSE, sq=FALSE)

Arguments

x Data matrix
method Dissimilarity index
keepdiag Compute amd keep diagonals
full Return the square dissimilarity matrix
sq Square the dissimilarities – useful for distance-based partitioning

Details

The function knows the following dissimilarity indices:
euclidean d[jk] = sqrt(sum (x[ij]-x[ik])^2)
manhattan d[jk] = sum(abs(x[ij] - x[ik]))
gower d[jk] = sum (abs(x[ij]-x[ik])/(max(i)-min(i))
canberra d[jk] = (1/NZ) sum ((x[ij]-x[ik])/(x[ij]+x[ik]))
bray d[jk] = (sum abs(x[ij]-x[ik])/(sum (x[ij]+x[ik]))
kulczynski d[jk] 1 - 0.5*((sum min(x[ij],x[ik])/(sum x[ij]) + (sum min(x[ij],x[ik])/(sum x[ik]))
maximum d[jk] = max(abs(x[ij] - x[ik]))
binary d[jk] = max(abs(x[ij]>0 - x[ik]>0))
chord d[jk] = sqrt((sum (x[ij]-x[ik])^2)/(sum (x[ij]+x[ik])^2))

where NZ is the number of non-zero entries.

Infamous ''double zeros'' are removed in Canberra dissimilarity.

Euclidean and Manhattan dissimilarities are not good in gradient separation without proper standardization but are still included for comparison and special needs.

Some of indices become identical or rank-order similar after some standardizations.

Value

Should be interchangeable with dist and returns a distance object of the same type.

Note

The function is an alternative to dist adding some ecologically meaningful indices. Both methods should produce similar types of objects which can be interchanged in any method accepting either. Manhattan and Euclidean dissimilarities should be identical in both methods, and Canberra dissimilary may be similar.

Author(s)

Jari Oksanen – modified Glenn De'ath (Dec 03)

References

Faith, D.P, Minchin, P.R. and Belbin, L. (1987) Compositional dissimilarity as a robust measure of ecological distance. Vegetatio 69, 57-68.

Examples

data(spider)
spider.dist <- gdist(spider[1:12,])

[Package mvpart version 1.2-6 Index]